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2 years ago

Solve the system of equations 2x+2y=6z=8 5x+6y+5z=3 5x+6y+3z=5

Mathematics

1 answer:

Alborosie2 years ago

4 0

Answer:

$x=34,y=-27andz=-1$

Step-by-step explanation:

Given:

$2x+2y+6z=8$ equation:1

$5x+6y+5z=3$ equation:2

$5x+6y+3z=5$ equation:3

We have to find the value of x,y and z

Eliminating two variables to find the value of third variable

Subtracting equation:2 from equation:3

$5x+6y+3z-(5x+6y+5z)=5-3$

$5x+6y+3z-5x-6y-5z=2\\-2z=2\\z=-1$

Solving the equation:1 for 'x'

$2x+2y+6z=8$

$2x=8-2y-6z\\2x=8-2y-6(-1)\\2x=8-2y+6\\2x=14-2y\\x=7-y$

Putting x and z in equation 2

$5(7-y)+6y+5(-1)=3\\35-5y+6y-5=3\\y+30=3\\y=3-30\\y=-27$

Putting the value of 'y' and 'z' in equation:2 to find the value of 'x'

$5x+6(-27)+5(-1)=3\\5x-162-5=3\\5x-167=3\\5x=3+167\\5x=170\\x=\frac{170}{5}\\ x=34$

The values of x,y and z are

$x=34,y=-27andz=-1$

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3 years ago

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A new sample of 225 employed adults is chosen. Find the probability that less than 7.1% of the individuals in this sample hold m

arsen [322]

Answer:

The probability that less than 7.1% of the individuals in this sample hold multiple jobs is 0.0043.

Step-by-step explanation:

Let X = number of individuals in the United States who held multiple jobs.

The probability that an individual holds multiple jobs is, p = 0.13.

The sample of employed individuals selected is of size, n = 225.

An individual holding multiple jobs is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 225 and p = 0.13.

But since the sample size is too large Normal approximation to Binomial can be used to define the distribution of proportion p.

Conditions of Normal approximation to Binomial are:

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Check the conditions as follows:

$np=225\times 0.13=29.25>10\\n(1-p)=225\times (1-0.13)=195.75>10$

The distribution of the proportion of individuals who hold multiple jobs is,

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Compute the probability that less than 7.1% of the individuals in this sample hold multiple jobs as follows:

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3 years ago

SOMEONE HELP ME ASAP!

lord [1]

Answer:

(-3, 1)

The solution is the point at which both lines intersect.

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

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To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using $\pi d$ or $2\pi r$ .

We write r: $\pi d$ or r: $2\pi r$ .

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3 years ago

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